To determine today's price of ABC, Inc.'s stock, we will use the Gordon Growth Model, also known as the Dividend Discount Model for a perpetuity with no growth. The formula for the price of a stock in this model is given by:
[tex]\[ P_0 = \frac{D}{r} \][/tex]
where:
- [tex]\( P_0 \)[/tex] is the current stock price.
- [tex]\( D \)[/tex] is the annual dividend.
- [tex]\( r \)[/tex] is the required rate of return.
Given:
- The annual dividend [tex]\( D \)[/tex] is $3.76.
- The required rate of return [tex]\( r \)[/tex] is 10.02%, or 0.1002 when expressed as a decimal.
Step-by-step solution:
1. Substitute the given values into the formula:
[tex]\[ P_0 = \frac{3.76}{0.1002} \][/tex]
2. Perform the division:
[tex]\[ P_0 = \frac{3.76}{0.1002} = 37.5249500998004 \][/tex]
3. Round the result to two decimal places:
[tex]\[ P_0 \approx 37.52 \][/tex]
Therefore, today's price of the stock is [tex]\( \mathbf{37.52} \)[/tex].
